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tigry1 [53]
3 years ago
15

verify that the fucntion satisfies the three hypotheses of rolles theorem on the given interval . then find all numbers c that s

atisfy the conclusion . f(x)= x^3-2x^2-4x+2 . [ -2,2]
Mathematics
1 answer:
Ghella [55]3 years ago
4 0

The roots of the polynomial <span><span>x^3 </span>− 2<span>x^2 </span>− 4x + 2</span> are:

<span><span>x1 </span>= 0.42801</span>

<span><span>x2 </span>= −1.51414</span>

<span><span>x3 </span>= 3.08613</span>


x1 and x2 are in the desired interval [-2, 2]

f'(x) = 3x^2 - 4x - 4

so we have:

3x^2 - 4x - 4 = 0

<span>x = ( 4 +- </span><span>√(16 + 48) </span>)/6

x_1 = -4/6 = -0.66

x_ 2 = 2

According to Rolle's theorem, we have one point in between:

x1 = 0.42801 and x2 = −1.51414

where f'(x) = 0, and that is <span>x_1 = -0.66</span>

so we see that Rolle's theorem holds in our function.

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Jane is having difficulty deciding whether to put her savings in the Mystic Bank or in the Four Rivers Bank. Mystic offers a 12%
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Jane must therefore deposit her savings in the four rivers bank.

<h3>What is compound interest?</h3>

Interest that is added to a loan and deposit sum is known as compound interest. In our everyday lives, it is the notion that is employed the most frequently. Compound interest is calculated as a sum using the interest and principal accrued over time. Compound interest versus simple interest differ primarily in this way.

As per the data provided in the question,

Rate, r = 12%

After five years, the total amount, if Jane had saved at Mystic Bank,if Jane had saved at Mystic Bank would be:

A = P(1+\frac{r}{100} )^n

For compounded quarterly,

n = 5 × 4

n = 20

A = 40000(1 + 12/(4 × 100))²⁰

A = 72244.44     (i)

If Jane placed her savings with the Four Rivers, then,

A = 40000(1 + 14/(2 × 100))¹⁰

A = 40000 × 1.9671

A = 78686.054  (ii)

Therefore, it is evident that case (ii) is higher than case (i). Jane must therefore deposit her savings in the four rivers bank.

To know more about Compound Interest:

brainly.com/question/29335425

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6 0
1 year ago
a mixture of peanuts and corn sells for P40 per kilo. The peanuts sell for P42 per kilo while the corn sells for P36 per kilo. h
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Answer:

The weight of peanuts in the mixture   = 8  kg

The weight of corns in the given mixture = 4 kg

Step-by-step explanation:

Let us assume the weight of peanuts in the mixture   = x kg

The weight if corns in the given mixture = y kg

Total weight = (x + y) kg

The combined mixture weight = 12 kg

⇒ x  + y = 12  ..... (1)

Cost of per kg if mixture  = $ 40

So, the cost of (x + y) kg mixture  = (x+y) 40 = 40(x+ y)   ..... (2)

 

The cost of 1 kg of peanuts =  $ 42

So cost of x kg of peanuts  = 42 (x)  = 42 x

The cost of 1 kg of corns  = $ 36

So cost of y kg of corns  = 36 (y)  = 36 y

So, the total cost of x kg peanuts  + y kg corns =  42 x +  36 y  .... (3)

From (1) and (2), we get:

40(x+ y)  = 42 x +  36 y

x +  y = 12 ⇒ y = 12 -x

Put this in  40(x+ y)  = 42 x +  36 y

We get:

40(x+ 12 -x)  = 42 x +  36 (12 -x)

480 = 42 x + 432 - 36 x

or, 480 - 432 = 6 x

or, x  = 8

⇒ y = 12 -x = 12 - 8 = 4

⇒  y = 4

Hence, the weight of peanuts in the mixture   = 8  kg

The weight of corns in the given mixture = 4 kg

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Step-by-step explanation:

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